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    "## Chapter 7 Linear multiclass classification"
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   "source": [
    "This notebook contains interactive content from an early draft of the university textbook <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main\">\n",
    "Machine Learning Refined (2nd edition) </a>.\n",
    "\n",
    "The final draft significantly expands on this content and is available for <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main/chapter_pdfs\"> download as a PDF here</a>."
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   "source": [
    "# 7.1 Introduction"
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    "In practice many classification problems have more than two classes we wish to distinguish, e.g., face recognition, hand gesture recognition, recognition of spoken phrases or words, etc. Such a multiclass dataset $\\left\\{ \\left(\\mathbf{x}_{p,}\\,y_{p}\\right)\\right\\} _{p=1}^{P}$ consists of $C$ distinct classes of data, where each label $y_{p}$ takes on one of $C$ distinct values.  In this Chapter we describe how to generalize what we have seen in the previous Chapter - where we dealt with two class classification - to deal with this multiclass setting.  In particular we will see two very popular methods for multiclass classification, called *One-versus-All* and *multiclass Softmax classification* (sometimes referred to as Softmax regression). "
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